Question: Express this quotient in scientific notation: ${\frac{2.130\times 10^{7}} {3.0\times 10^{3}}}$
Solution: Start by collecting like terms together. $= {\frac{2.130} {3.0}} \times{\frac{10^{7}} {10^{3}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.71 \times 10^{7\,-\,3}$ $= 0.71 \times 10^{4}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.71$ is the same as $7.10 \div 10$ , or $7.10 \times 10^{-1}$ $ = {7.10 \times 10^{-1}} \times 10^{4} $ $= 7.10\times 10^{3}$